1. GCF/LCM
Module2
Lesson 18

2. Lesson 18
I can find the least common multiple and greatest common factor and apply knowledge of factors to use the distributive property.

3. The greatest common factor of two whole numbers (not both zeros) is the greatest whole number that is a factor of each number. The greatest common factor of two whole numbers a and b is denoted by GCF (a,b).
The least common multiple of two whole numbers is the smallest whole number greater than zero that is a multiple of each number. The least common multiple of two whole numbers a and b is denoted by LCM (a,b).

4. Find the Greatest Common Factor of 12 and 18.
Find the Least Common Multiple of 12 and 18
List the factors starting with 1:
List the multiples 1 12 1 18

5. Another way to find the greatest common factor and the least common multiple
The Ladder Method
GCF of 12 and LCM of 12 and 18
12 , 18
12 , 18

6. Find the Prime Factorization of 12 and 18
Another way to find the Greatest Common Factor and the least Common Multiple
Find the Prime Factorization of 12 and 18
GCF:
LCM:

7. Find the GCF and LCM of 30 and 50 Try all three methods

8. Find the GCF and LCM of 24 and 60 Try all three methods

9. Find the GCF and LCM of 15 and 45 Try all three methods

10. Find the GCF and LCM of 42 and 70 Try all three methods

11. GCF for 26,48, and 62

12. There are 18 girls and 24 boys who want to participate in a Trivia Challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter? How many boys and girls will be on each team?

13. Ski club members are preparing identical welcome kits for new skiers
Ski club members are preparing identical welcome kits for new skiers. The Ski Club has 60 hand-warmer packets and 48 foot-warmer packets. Find the greatest number of identical kits they can prepare using all of the hand-warmers and foot-warmer packets. How many hand-warmer and foot-warmer packets would each welcome kit have?

14. Hot dogs come packed 10 in a package
Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic with none left over, what is the least amount of each we need to buy? How many packages of each item would we have to buy?

15. Starting at 6:00am, a bus stops at my street corner every 15 minutes
Starting at 6:00am, a bus stops at my street corner every 15 minutes. Also starting at 6:00am, a taxi cab comes by every 12 minutes. What is the next time both a bus and a taxi are at the corner at the same time?

16. There are 435 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress if we want the largest groups possible? How many representatives and senators would be in each group?

17. Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has 24 teeth, and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again?

18. Is the GCF of a pair of numbers ever greater than both numbers?
Is the GCF of a pair of numbers ever equal to one of the numbers? Explain and if possible give an example.
Is the GCF of a pair of numbers ever greater than both numbers?
Explain and if possible give an example.

19. Is the LCM of a pair of numbers ever less than both numbers?
Is the LCM of a pair of numbers ever equal to one of the numbers? Explain and if possible give an example.
Is the LCM of a pair of numbers ever less than both numbers?
Explain and if possible give an example.

20. https://youtu.be/jFd-6EPfnec - GCF explained
- GCF/LCM ladder method
- LCM with prime factorization
- GCF with prime factorization